So, for those who haven't read the Ulster Cycle consider this a slightly abridged re-telling of the Morrigan's interactions with Cu Chulainn, beginning with the encounter that sets up their encounters in the Tain Bo Cuiligne
In the Tain Bo Regamna....
Cu Chulainn wakes up to the sound of a cow bellowing. Leaping out of bed naked he runs outside with his wife Emer chasing him carrying his clothes. He yells to his charoiteer, Laeg, to ready their chariot and they go to find out what all the hubbub is about. After a short ride they come upon a strange sight: a chariot pulled by a one legged red horse, with the chariot post affixed through the horses body and forehead. In the chariot is a red haired woman wearing a red cloak which trails to the ground; next to it is a large man using a hazel rod to drive a cow who is bellowing.
Cu Chulain points out that the cow doesn't like the way she's being driven and the woman replies that its none of his business because its not his cow, or his friend's cow. Cu Chulainn then says that it is his business because every cow in Ulster is his business, to which the woman replies that he takes on a lot. He then asks why she is talking to him and the man isn't and she says because she's the one he yelled at. He then says that when she speaks she speaks for the man and she replies by giving the man's name as "Cold wind-conflict-brightness-strife". Cu Chulainn remarks that this is a wondrous name and asks if she is going to speak for him the whole time and what her name is, at which point the man speaks, and tells him that the woman's name is "Keen edged-small lipped-plain cloaked-hair-sharp shouting-fierceness-a phantom"
Cu Chulain gets pissed at this point and accuses them of trying to make a fool of him, then leaps onto the woman in the chariot and holds a spear to her head, asking her who she really is.
She tells him that she is a satirist and that the cow was payment for a poem, given to her by Daire mac Fiachnai of Cuiligne. So Cu Chulainn says that he wants to hear her recite a poem and she says she will if he will get off of her, which he does, jumping down between the chariot poles.
She proceeds to recite a poem against him and he leaps into his own chariot only to find that the woman, cow, and man have disappeared and only a black bird remains perched in a tree nearby.
He calls her a hurtful woman and she says that the place they are at will be named 'Bog of Distress' because of his words.
He says if he knew who he was talking to they wouldn't have parted that way and she pledges that whatever he would have done it would still have ended badly for him. He then says that she has no power over him, to which she replies that she does indeed, and that she is bringing and will bring his death; she then explains that she has brought the cow from out of the Sidhe of Cruachan to be bred by the Brown Bull of Cuiligne and that the calf it carries will start a great cattle raid, and implies that Cu Chulainn will die in this raid. He of course replies that he will not be killed and that he will become enormously famous in this cattle raid.
She then promises to wait until he is fighting a skilled opponent, who is his equal in all ways, and then she will come to him as an eel in the ford to trip him so that he will be fighting an unfair fight. He replies that he will dash her against a stone to break her ribs and that she won't be healed unless he himself blesses her.
She then promises to come at him as a wolf and tear a strip from his arm during the fighting so that the odds will be really unfair, to which he replies that he will wound her eye with his spear and she won't be healed until he blesses her.
Finally she says she will appear as a red-eared white heifer driving fifty other cows before her into the ford and the fight will be so unfair that he will be killed and his head taken as a trophy. He pledges to break her leg with a sling stone and that she won't be healed unless he blesses her, which he will not do.
The two then go their separate ways.